Fans of niche sports generally find minimal content in mainstream media due to their limited audience. Instead, social media offers them the opportunity to follow these specific sports. The dynamics behind digital media are based on individual participation, hence some prominent users lead the social conversation thanks to their capacity to influence. However, the complexity of the concept of influence and the existence of multiple parameters for its measurement make it difficult to identify these key users. Our research proposes a measure of the influence on Twitter based on variables derived from the platform (number of tweets, number of retweets, and number of followers) and from the Social Network Analysis (outdegree, indegree, and PageRank). The Analytic Hierarchy Process was used to assign a weight to each variable. This measure of influence was applied to the conversation generated on Twitter around a niche sporting event: the 2018 UCI Track Cycling World Championships. From a 19 701-tweet corpus, we identified the 25 most influential users. The results indicate that the organisers and the participating cyclists played a relevant role in the Twitter conversation. In addition, the geographic distribution of these influential users reflects the cultural dependence of niche sports.